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What is the Least Common Multiple of 29696 and 29700?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 29696 and 29700 is 220492800.

LCM(29696,29700) = 220492800

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Least Common Multiple of 29696 and 29700 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 29696 and 29700, than apply into the LCM equation.

GCF(29696,29700) = 4
LCM(29696,29700) = ( 29696 × 29700) / 4
LCM(29696,29700) = 881971200 / 4
LCM(29696,29700) = 220492800

Least Common Multiple (LCM) of 29696 and 29700 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 29696 and 29700. First we will calculate the prime factors of 29696 and 29700.

Prime Factorization of 29696

Prime factors of 29696 are 2, 29. Prime factorization of 29696 in exponential form is:

29696 = 210 × 291

Prime Factorization of 29700

Prime factors of 29700 are 2, 3, 5, 11. Prime factorization of 29700 in exponential form is:

29700 = 22 × 33 × 52 × 111

Now multiplying the highest exponent prime factors to calculate the LCM of 29696 and 29700.

LCM(29696,29700) = 210 × 291 × 33 × 52 × 111
LCM(29696,29700) = 220492800